A:AnswerYes you will be able to use the whole screen with your PlayStation 4. However the screen will be stretched as the PlayStation is not meant to play at those dimensions. Games are still very much playable after you adjust to the slight stretching of the image.
A:AnswerIt would run it perfectly fine. My i9 16gb ram evga 2070 super work perfectly fine, only thing I really have to do is cap most games to 144 FPS.
A:AnswerYes, you can hook this monitor to anything that has an HDMI or DP output. However, Xbox One and PS4 do not support aspect ratios larger than 16:9, which is a standard TV and monitor ratio. You essentially would have large black bars on either side of the monitor turning this into a VERY expensive 1080P 24”(ish) monitor.